Multiplying Fractions

Learning Objective:

• we are learning to multiply fractions
• success criteria: after learning this topic you will be able to:
  • multiply fractions accurately and quickly
  • explain how to multiply fractions to someone else.
• graded example questions:

$\quad \dfrac {1}{3} \times \dfrac {1}{4} = \\$
$\quad \dfrac {2}{7} \times \dfrac {5}{9} = \\$
$\quad \dfrac {4}{5} \times \dfrac {1}{6} = \\$
$\quad \dfrac {11}{4} \times \dfrac {8}{7} = \\$
$\quad \dfrac {a}{b} \times \dfrac {c}{d} = \\$
$\quad \frac {3}{5} \times 7 \frac {1}{2} = \\$

Investing:

• This skill is useful because you may wish to work out one fraction of another, such as one third of three-fifths.
• Functional (real-life) applications include:
  • I recently wanted to work out the nutritional content of some food I ate. I had three-fifths of the chilli I made using seven-and-a-half tablespoons of kidney beans. How many tablespoons of beans in my portion? How many calories is that?
  • I am designing a garden wall using reclaimed vintage British Imperial bricks to match my house. I want to design an elegant and interesting brick bond to be the backdrop to an impressive flower bed. I find out that old bricks measure 8½ × 4 × 2½ in and I set out to draw my design on paper at one-fifth scale. How big should each dimension of the brick be on paper? What design looks good?
  • It is 15½°C outside today. A friend in America asks how much this is in Fahrenheit. A search on the internet gives the formula

$\quad F = \dfrac{9}{5} C + 32$

• This skill leads to:
  • dividing fractions
  • fractional change (increasing and decreasing by a fraction)
  • finding the probablility of two independent events
  • manipulating algebra including fractions
  • solving equations with fractional coefficients
  • fractional scale-factor enlargement
• A 'free gift' with this skill is that we can now also find a fraction of an amount by treating whole numbers and decimals as fractions.
• This could help you if you want to work in design, engineering, science, ...

Preparing:

• Are we ready?
  • Can you already multiply small whole-numbers?
  • Do you know your times-tables?
  • Do you know the times-tables back to front?
• Let's be sure you can answer these aloud or on a mini-whiteboard if you're in a classroom.
• You will have a deeper understanding if you also know the relationship between multiplication and reciprocals.

Discovering:

• Can you figure it out yourself from these examples?

$\dfrac{2}{3} \times \dfrac{5}{7} = \dfrac{10}{21}$

$\dfrac{2}{5} \times \dfrac{4}{9} = \dfrac{8}{45}$

$\dfrac{3}{4} \times \dfrac{2}{11} = \dfrac{6}{44} = \dfrac{3}{22}$

• Try to predict the next one aloud or on a mini-whiteboard.
• Investigate...

Modeling:

• Here are some examples of people getting it right:
• Here are some examples of people getting it wrong in typical ways:
• Here are some more examples. Did they get it right or wrong? Explain how you know!

Discussing:

• What would this one be? Tell your learning partner. Convince them you're right.
• Explain how you know.
• How would you explain this to someone who was new to it?

Explaining:

• One way to do this is...
• Another approach might be...
• A useful shortcut is to...
• This works because...
• It doesn't work when...
• An exception is...
• Watch out for...
• A common mistake is...
• You can check your result by...
• We can prove this works by...

Practicing:

• Some straightforward examples can be found in Heinemann Intermediate Practice Book, Exercise 11.5, questions 1a to 1h
• Some harder examples including mixed numbers in Heinemann Intermediate Practice Book, Exercise 11.5, questions 1i to 1l
• Some application of this skill to (semi-) functional contexts in Heinemann Intermediate Practice Book, Exercise 11.5, questions 2 onward.
• Solutions to these exercises are here:
  

  Multiplying & Dividing Fractions - consolidation.jnt
  

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• Some mixed examples.
• Some non-examples to spot and some mixed questions with redundant, insufficient or contradictory data.
• You can demonstrate fluency by at least...

Sharing:

• A web page or wiki I have created to explain this can be found at...
• A presentation I have created and rehearsed looks like...
• A poster I have drawn or model I have made can be found...

Assessing:

• Check you've mastered this skill by...
• Show you understand by explaining...
• Prove you're an expert in... by...

Developing:

• Next we could learn...
• This leads to...
• Now try...

Boardwork:

last edited: Oct 1, 2013 2:52 am